It's empty because there is nothing in it

I don't have a problem with the Shroud of Turin. Its claim to be the burial shroud of Jesus doesn't get past the first word. Assuming that the Crucifixion took place more or less as described, Jesus wasn't buried. Pontius Pilate was a strict military governor (in fact, called home once for being overly severe), so he isn't going to break an easy rule. In three hundred years of continuous conquest, the Romans had learned that leaving a tomb -- or any other visible reminder -- of a charismatic rebel leader just leads to a prolonged or recurring rebellion. So, he would not have agreed to Joseph's request, even if Joseph had been fool enough to make it -- admitting friendship with a just executed rebel leader was grounds for arrest and at least a beating.

"But all the texts agree that Jesus was buried." Well, yes, because you need a burial to get a resurrection (if a body got up from the garbage heap where the crucified were tossed, no one would notice or could point to the evidence that one was missing). And the resurrection was necessary to complete, make sense of, the crucifixion. Which is somehow necessary for our salvation (though just how is hard to answer in a way consistent with other theological points).

Of course, the resurrection presents its own problems as well. If Jesus' body was resuscitated, it is a very strange body indeed. The inevitable damage from being dead 36 hours has been repaired, though not the external wounds. It can eat and break bread and be felt, but it can also pass through walls or, more likely, port to or from any place. And it does not seem to be in continuous existence, for there are long stretches when no one knows where it is (I will pass over the levitation at the end). Once you allow all that, the difference from a vision seems mostly verbal. And Paul, who never claims more than a vision, still claims that what he had was the same as what the Twelve and Mary and all had.

But the question is still, what does all this or any part of it have to do with our salvation?